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A pseudospectral method for the one-dimensional fractional Laplacian on R

Author

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  • Cayama, Jorge
  • Cuesta, Carlota M.
  • de la Hoz, Francisco

Abstract

In this paper, we propose a novel pseudospectral method to approximate accurately and efficiently the fractional Laplacian without using truncation. More precisely, given a bounded regular function defined over R, we map the unbounded domain into a finite one, and represent the resulting function as a trigonometric series. Therefore, the central point of this paper is the computation of the fractional Laplacian of an elementary trigonometric function.

Suggested Citation

  • Cayama, Jorge & Cuesta, Carlota M. & de la Hoz, Francisco, 2021. "A pseudospectral method for the one-dimensional fractional Laplacian on R," Applied Mathematics and Computation, Elsevier, vol. 389(C).
    • Handle: RePEc:eee:apmaco:v:389:y:2021:i:c:s0096300320305336
    DOI: 10.1016/j.amc.2020.125577
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    References listed on IDEAS

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    1. Khader, M.M. & Saad, K.M., 2018. "A numerical approach for solving the fractional Fisher equation using Chebyshev spectral collocation method," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 169-177.
    2. Hans Engler, 2010. "On the Speed of Spread for Fractional Reaction-Diffusion Equations," International Journal of Differential Equations, Hindawi, vol. 2010, pages 1-16, November.
    3. Olmos, Daniel & Shizgal, Bernie D., 2009. "Pseudospectral method of solution of the Fitzhugh–Nagumo equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2258-2278.
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